Dielectric tunability of BaxSr1 − xTiO3 thin films grown on a compliant substrate

The phase transition temperature and dielectric tunability of Ba_xSr_1-xTiO₃ (BST) thin films grown on a compliant substrate are theoretically investigated using the Ginzburg-Landau-Devonshire theory combined with the Timosheko elastic theory by considering thin films´ and substrates´ thickness-dependent relaxation of lattice-mismatch strain. Our results indicate that the dielectric characteristics of BST thin films deposited on compliant substrates are different from those of their bulk counterparts. The ferroelectricity and dielectric performances of the BST thin films can be modulated by changing the thickness ratio of the film to substrate or the stress state. This is an effectively theoretical guidance for the property optimization of ferroelectric thin films used in microwave devices.